automorphism's Usage Examples:

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

In mathematics, the automorphism group of an object X is the group consisting of automorphisms of X.

Further equivalent definitions of Dn are: The automorphism group of the graph consisting only of a cycle with n vertices (if n ≥.

In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the.

the automorphism group of An is the symmetric group Sn, with inner automorphism group An and outer automorphism group Z2; the outer automorphism comes.

In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the.

any algebraic version of E6 is the cyclic group Z/3Z, and its outer automorphism group is the cyclic group Z/2Z.

automorphism group, because 36 ≡ 1 (modulo 7), while lower powers do not give 1.

Thus this automorphism generates Z6.

There is one more automorphism with.

their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory.

In mathematics, the outer automorphism group of a group, G, is the quotient, Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is.

obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.

isomorphism from a partially ordered set to itself is called an order automorphism.

[citation needed] An automorphism is an isomorphism from a structure to itself.

endomorphism is a lattice homomorphism from a lattice to itself, and a lattice automorphism is a bijective lattice endomorphism.

In certain contexts it is an automorphism, but this is not true in general.

any algebraic version of E7 is the cyclic group Z/2Z, and its outer automorphism group is the trivial group.

in the sense that its birational automorphism group is finite.

At the other extreme, the birational automorphism group of projective space P n {\displaystyle.

their order, the size of the Schur multiplier, the size of the outer automorphism group, usually some small representations, and lists of all duplicates.

An endomorphism that is also an isomorphism is an automorphism.